# Solving for base angles in a congruent triangle

## Homework Statement

Solving for base angles in a congruent triangle
One of the base angles in a congruent triangle is 3x+5
The other base angle is unknown
The remaining angle is x+16.

See attached PDF

## The Attempt at a Solution

Because two base angles in a congruent triangle are the same and I have been given one of them I did the following:-

3x+5 = 3x+5 (I then tried to solve for x but this cancels out to 0.)

I want to know why this is the case, i think it is because i have 2 unknown variables but only1 equation.

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Dick
Homework Helper

## Homework Statement

Solving for base angles in a congruent triangle
One of the base angles in a congruent triangle is 3x+5
The other base angle is unknown
The remaining angle is x+16.

See attached PDF

## The Attempt at a Solution

Because two base angles in a congruent triangle are the same and I have been given one of them I did the following:-

3x+5 = 3x+5 (I then tried to solve for x but this cancels out to 0.)

I want to know why this is the case, i think it is because i have 2 unknown variables but only1 equation.
As you said, the other base angle is 3x+5. You need to use something else. What's the sum of all of the angles of a triangle?

The sum of the interior angles of a triangle is 180Degrees.

But i want to know if making 3x+5 equal to itself 3x+5 (3x+5 = 3x+5) am i trying to solve for 1 unknown with 1 equation or am i trying to solve 2 unknowns with 1 equations?

SteamKing
Staff Emeritus
Homework Helper
Setting 3x + 5 equal to itself implies 1 = 1. You need some other piece of information.

Dick
Homework Helper
The sum of the interior angles of a triangle is 180Degrees.

But i want to know if making 3x+5 equal to itself 3x+5 (3x+5 = 3x+5) am i trying to solve for 1 unknown with 1 equation or am i trying to solve 2 unknowns with 1 equations?
As you said, the sum of your angles is 180 degrees. Write down an equation that expresses that.

Curious3141
Homework Helper
Also, why are you calling it a "congruent triangle"? Don't you mean "isoceles triangle"?

To expand on what others have said, what is the sum of the 3 angles in terms of x? Equate that expression to 180 degrees and solve.